High stability angular sensor

ABSTRACT

An angular rate sensor. The sensor includes a Coriolis vibratory gyroscope (CVG) resonator, configured to oscillate in a first normal mode and in a second normal mode; a frequency reference configured to generate a reference signal; and a first phase control circuit. The first phase control circuit is configured to: measure a first phase difference between: a first phase target, and the difference between: a phase of an oscillation of the first normal mode and a phase of the reference signal. The first phase control circuit is further configured to apply a first phase correction signal to the CVG resonator, to reduce the first phase difference. A second phase control circuit is similarly configured to apply a second phase correction signal to the CVG resonator, to reduce a corresponding, second phase difference.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present application is a continuation of U.S. patent applicationSer. No. 15/253,704, filed Aug. 31, 2016, entitled “HIGH STABILITYANGULAR SENSOR”, which claims priority to and the benefit of U.S.Provisional Application No. 62/212,902, filed Sep. 1, 2015, entitled“ATOM LOCKED ANGULAR SENSOR (ATLAS) WITH HIGH RESOLUTION AND DYNAMICRANGE MULTI-MODE GYRO (MMG) ARCHITECTURE”, and priority to and thebenefit of U.S. Provisional Application No. 62/321,042, filed Apr. 11,2016, entitled “STABILIZATION OF CORIOLIS VIBRATORY GYROSCOPES BYFREQUENCY LOCKING TO ULTRA STABLE CLOCKS”. The entire contents of alldocuments identified in this paragraph are hereby incorporated herein byreference as if fully set forth herein.

FIELD

One or more aspects of embodiments according to the present inventionrelate to angular sensors, and more particularly to a high stabilityangular sensor.

BACKGROUND

Gyroscopes may be used in a wide range of applications, includingguidance of aircraft, spacecraft, missiles, and the like. A gyroscope(or “gyro”) measures an angular rate, i.e., the rate at which thegyroscope rotates, about one or more axes. The output of a gyroscope maybe an analog signal or a digital data stream, and it may include, alongwith an indication of the angular rate of the gyro, noise or errors. Forexample, the gyroscope may have a bias, e.g., it may indicate a non-zeroangular rate when it is not rotating. The bias may vary with time,exhibiting an error referred to as bias drift. Bias drift may limit theusefulness of a gyroscope for guidance applications, especially whenother sensors with better low-frequency performance are not available tocomplement the gyro.

Thus, there is a need for a gyroscope with reduced bias drift.

SUMMARY

According to an embodiment of the present invention there is provided anangular sensor, including: a Coriolis vibratory gyroscope (CVG)resonator, configured to oscillate in a first normal mode and in asecond normal mode; a frequency reference configured to generate areference signal; and a first phase control circuit configured to:measure a first phase difference between: a first phase target, and thedifference between: a phase of an oscillation of the first normal modeand a phase of the reference signal; apply a first phase correctionsignal to the CVG resonator, to reduce the first phase difference; and asecond phase control circuit configured to: measure a second phasedifference between: a second phase target, and the difference between: aphase of an oscillation of the second normal mode and the phase of thereference signal; and apply a second phase correction signal to the CVGresonator, to reduce the second phase difference.

In one embodiment, the first phase target and the second phase targetare programmable.

In one embodiment, the first normal mode and the second normal mode arenominally degenerate.

In one embodiment, the angular sensor includes a first amplitude controlcircuit configured to: measure a first amplitude difference between: afirst amplitude target, and the amplitude of the oscillation of thefirst normal mode, and apply a first amplitude correction signal to theCVG resonator, to reduce the first amplitude difference.

In one embodiment, the angular sensor includes a second amplitudecontrol circuit configured to: measure a second amplitude differencebetween: a second amplitude target, and the amplitude of the oscillationof the second normal mode, and apply a second amplitude correctionsignal to the CVG resonator, to reduce the second amplitude difference.

In one embodiment, the first amplitude target and the second amplitudetarget are programmable.

In one embodiment, the first amplitude target is about 1/10th of thesecond amplitude target.

In one embodiment, the first amplitude control circuit, and the secondamplitude control circuit are configured to interchange the values ofthe first amplitude target and the second amplitude target duringoperation.

In one embodiment, the first amplitude control circuit, and the secondamplitude control circuit are configured to interchange the values ofthe first amplitude target and the second amplitude target repeatedlyduring operation.

In one embodiment, the frequency reference includes an atomic frequencyreference.

In one embodiment, the atomic frequency reference is a rubidium clock.

In one embodiment, the atomic frequency reference is a chip-scale atomicclock (CSAC).

In one embodiment, the first phase control circuit is configured toapply a first phase correction signal to the CVG resonator by adjustinga natural frequency of the first normal mode.

In one embodiment, the first phase control circuit is configured toadjust the natural frequency of the first normal mode by applying a biasvoltage to a first tuning electrode of the CVG resonator.

In one embodiment, the second phase control circuit is configured toadjust a natural frequency of the second normal mode by applying a biasvoltage to a second tuning electrode of the CVG resonator.

In one embodiment, the angular sensor includes a first amplitude controlcircuit configured to: measure a first amplitude difference between: afirst amplitude target, and the amplitude of the oscillation of thefirst normal mode, and apply a first amplitude correction signal to theCVG resonator, to reduce the first amplitude difference.

In one embodiment, the angular sensor includes a second amplitudecontrol circuit configured to: measure a second amplitude differencebetween: a second amplitude target, and the amplitude of the oscillationof the second normal mode, and apply a second amplitude correctionsignal to the CVG resonator, to reduce the second amplitude difference.

In one embodiment, the first amplitude target and the second amplitudetarget are programmable.

In one embodiment, the first amplitude target is about 1/10th of thesecond amplitude target.

In one embodiment, the first amplitude control circuit, and the secondamplitude control circuit are configured to interchange the values ofthe first amplitude target and the second amplitude target duringoperation.

In one embodiment, the angular sensor includes: a plurality of theangular sensors, configured to share a common frequency reference.

According to an embodiment of the present invention there is provided amethod for operating an angular sensor a including a Coriolis vibratorygyroscope (CVG) resonator, configured to oscillate in a first normalmode and in a second normal mode and a frequency reference configured togenerate a reference signal, the method including: measuring a firstphase difference between: a first phase target, and the differencebetween: a phase of an oscillation of the first normal mode and a phaseof the reference signal; applying a first phase correction signal to theCVG resonator, to reduce the first phase difference; and measuring asecond phase difference between: a second phase target, and thedifference between: a phase of an oscillation of the second normal modeand the phase of the reference signal; and applying a second phasecorrection signal to the CVG resonator, to reduce the second phasedifference.

According to an embodiment of the present invention there is provided aacceleration and/or magnetic sensor, including: an acceleration ormagnetic field sensitive MEMS resonator, configured to oscillate in atleast a first normal mode; a frequency reference configured to generatea reference signal; and at least a first phase control circuitconfigured to: measure a first phase difference between: a first phasetarget, and the difference between: a phase of an oscillation of thefirst normal mode and a phase of the reference signal; and apply a firstnatural frequency control signal to the MEMS resonator, to reduce thefirst phase difference.

In one embodiment, the first phase target is programmable.

In one embodiment, the natural frequency control signal is a biasvoltage on a first tuning electrode of the MEMS resonator.

In one embodiment, a sensor cluster includes a plurality of the sensors,configured to share a common frequency reference.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features and advantages of the present invention will beappreciated and understood with reference to the specification, claims,and appended drawings wherein:

FIG. 1 is an illustration of a Coriolis vibratory gyroscope (CVG)resonator, according to an embodiment of the present invention;

FIG. 2 is a block diagram of a high stability angular sensor, accordingto an embodiment of the present invention;

FIG. 3 is a detailed block diagram of the high stability angular sensorof FIG. 2;

FIG. 4 is a block diagram of a high stability angular sensor, accordingto another embodiment of the present invention;

FIG. 5A is a frequency diagram of an angular sensor, according to anembodiment of the present invention;

FIG. 5B is a frequency diagram of an angular sensor, according to anembodiment of the present invention;

FIG. 6 is an Allan deviation chart of an angular sensor, according to anembodiment of the present invention;

FIG. 7 is an illustration of normal modes with different mode numbers,according to an embodiment of the present invention; and

FIG. 8 is block diagram of a high stability, high dynamic range angularsensor, according to an embodiment of the present invention.

DETAILED DESCRIPTION

The detailed description set forth below in connection with the appendeddrawings is intended as a description of exemplary embodiments of a highstability angular sensor provided in accordance with the presentinvention and is not intended to represent the only forms in which thepresent invention may be constructed or utilized. The description setsforth the features of the present invention in connection with theillustrated embodiments. It is to be understood, however, that the sameor equivalent functions and structures may be accomplished by differentembodiments that are also intended to be encompassed within the spiritand scope of the invention. As denoted elsewhere herein, like elementnumbers are intended to indicate like elements or features.

Referring to FIG. 1, in one embodiment a disk resonator gyroscope (DRG)or other Coriolis vibratory gyroscope (CVG) may include a resonator suchas a disk 105, with a plurality of resonator electrodes, and a case orsubstrate 107 that may include a plurality of housing electrodes, eachin proximity with a corresponding resonator electrode. The disk 105 maybe secured by an anchor 108. The pairs of corresponding electrodes (oneelectrode of each pair being a resonator electrode, and the other beinga corresponding housing electrode) may be parallel and havesubstantially the same size and shape, and each pair of correspondingelectrodes may form a parallel plate capacitor. The application of afirst voltage to a resonator electrode and of a second voltage to acorresponding housing electrode may result in a potential differencebetween the two electrodes and an electric field in the region betweenthe electrodes. Opposite charges on the surfaces of the two electrodesmay attract, so that an attractive force is exerted on the resonatorelectrode by the housing electrode. If the voltage varies with time,then the attractive force may vary with time, and, for example, atime-varying force applied at a drive frequency near the frequency of afirst normal mode of the resonator may cause the resonator oscillate inthe first mode, i.e., to deform, with relatively large amplitude, at thedrive frequency, in motion corresponding to the shape of the firstnormal mode.

Pairs of electrodes may also be used to detect the displacement of aportion of the resonator with respect to the housing. For example, if aDC voltage is applied to a pair of electrodes, then the change incapacitance resulting from a change in separation between the electrodesmay cause a current to flow onto one electrode of the pair and an equalcurrent to flow away from the other electrode of the pair. Such acurrent may be amplified, for example, with a transimpedance amplifier(TIA).

For example, as illustrated in FIG. 1, the resonator may have 16electrodes including a first drive electrode 110, a second driveelectrode 115, a first sense electrode 120, and a second sense electrode125. A first n=2 mode having a first mode shape 130 may be driven by thefirst drive electrode 110 and sensed by the first sense electrode 120,and a second n=2 mode having a second mode shape 135 may be driven bythe second drive electrode 115 and sensed by the second sense electrode125. In some embodiments more than one electrode may be drivensimultaneously or concurrently to drive a particular mode, and/or morethan one electrode may be sensed simultaneously or concurrently to sensedisplacement in a particular mode.

If the first mode of the resonator is driven and the resonator isrotated (e.g., about an axis perpendicular to the disk, in the case ofthe disk-shaped resonator), the mechanical energy in the driven firstnormal mode may couple into a second normal mode having the same modenumber and a mode shape that is rotated, e.g., by 45 degrees, relativeto the mode shape of the first mode. The rate of coupling may beproportional to the rate of rotation.

The first and second normal modes may be nominally degenerate, e.g., ina disk resonator they may correspond to modes that would be perfectlydegenerate (i.e., that would have the same natural frequency) if thedisk resonator shape, material, and boundary conditions had perfectcylindrical symmetry. The natural frequencies of the first and secondnormal modes may differ, because, for example, the disk resonator maynot be perfectly circular.

The attractive force due to a potential difference across the twoelectrodes may also vary with the separation of the electrodes, e.g.,due to fringing fields at the edges of the electrodes and because, ifthe potential difference is constant, the change in capacitance withseparation may result in a change in the charge on the electrodes. Thisvariation in force with distance may have the effect of an additional(negative) spring force superimposed on the mechanical internalrestoring force of the resonator, so that a DC voltage applied to anypair of electrodes may affect (e.g., lower) the natural frequency of thefirst and/or second normal mode.

If a gyroscope is operated as described above, with the first normalmode being driven, and the coupling of energy into the second normalmode used as a measure of the rotation of the gyro, then the bias of thegyroscope may have a term that is proportional to the variation of thedrive frequency (from a nominal frequency). The gyroscope biasuncertainty term may be derived from the Allan deviation of thegyroscope rate output as:

${B(\tau)} = {{\sigma_{\Omega}(\tau)} = {\frac{90}{k}\frac{2\; f\;{\sigma_{y}(\tau)}}{Q}}}$

with2fσ_(y)(τ)≈Δf

where B(τ) is the gyroscope bias instability, k is the gyroscope scalefactor (angular gain), f is the drive frequency, and σ_(y)(τ) is theAllan deviation or instability of the fractional frequency of the drivefrequency. Since the two normal modes are both driven by f, theinstability of the residual frequency split between them will be boundedby Δf≈2fσ_(y)(τ), where the factor of 2 accounts for the instability ofeach normal mode. As such, a system employing a stable drive frequencymay exhibit a stable bias.

Accordingly, in one embodiment, a highly stable frequency reference 210is used in a gyroscope system as illustrated in FIG. 2, to achieve highbias stability. Two amplitude and phase control loops 215, 220 controlthe amplitude and phase of the first and second mode of the DRG,respectively. In some embodiments, the first stable frequency reference210 is shared by multiple sensor systems, e.g., it is shared by threegyroscopes that are combined to form a three-axis gyroscope.

Referring to FIG. 3, in one embodiment the resonator may be outfittedwith a first sense electrode 120 and a first drive electrode 110,coupled to the first mode of the resonator. The first control loop mayinclude a first transimpedance amplifier (TIA) 305 connected to thefirst sense electrode 120, a first analog to digital converter 310, afirst automatic gain control block 315, a first phase locked loop block320, a first digital to analog converter 325, and a first driver 330.The first transimpedance amplifier 305 (TIA), the first analog todigital converter 310, the first digital to analog converter 325, andthe first driver 330 may be part of a digital to analog conversion andanalog signal conditioning circuit 350. The first automatic gain controlblock 315 and the first phase locked loop block 320 may be part of adigital control and synthesis circuit 352, which may be an entirelydigital circuit, implemented, for example, in a field-programmable gatearray (FPGA). The frequency reference may include a first stablefrequency reference 335 (such as a rubidium atomic clock, or achip-scale atomic clock such as the system described in the followingpublication: R. Lutwak, et al. “The Chip-Scale Atomic Clock—RecentDevelopment Progress”, Proceedings of the 35^(th) Annual Precise Timeand Time Interval (PTTI) Systems and Applications Meeting, Dec. 2-4,2003, San Diego, Calif., pp. 467-478), operating at a relatively highinternal frequency, e.g., 10 MHz. A frequency divider 340 may divide thefrequency down to a frequency, at the output of the frequency reference210, that is near the natural frequencies of the first and second normalmodes, e.g., 20 kHz. The frequency reference 210 may also include areference voltage generator 345. In operation, the first mode may, inresponse to drive signals applied by the first control loop, oscillateat the frequency reference output frequency, e.g., 20 kHz. In oneembodiment, the first TIA 305 generates a signal proportional to thedisplacement of the disk in the first mode, and the first analog todigital converter 310 generates from it a digital data streamrepresenting the displacement of the disk in the first mode. The firstautomatic gain control block 315 measures the amplitude of the motion,compares it to a target (or “setpoint”) value (e.g., a pre-programmedoperating amplitude), generates an amplitude error signal proportionalto the difference between the amplitude of the motion and the target,and generates an amplitude correction signal from the amplitude errorsignal. The amplitude correction signal may be generated, for example,by processing the amplitude error signal with a loop filter and aproportional-integral-differential (PID) controller. In someembodiments, the loop filter follows a demodulator (in the phasedetector or amplitude detector) to set the loop bandwidth, and the loopfilter may be considered as part of the detector. The loop filter isthen followed by one or more additional elements, such as a PIDcontroller or other controller to generate the control signal from theerror signal.

In a parallel path, the output from the first analog to digitalconverter 310 may also be processed by the first phase locked loop block320 to measure the phase error of the displacement of the DRG in thefirst mode, and to generate a corresponding correction signal andsinusoidal drive signal. For example, the first phase locked loop block320 may control the phase of the displacement of the disk in the firstmode to be substantially in phase with the frequency reference outputsignal as follows. The first phase locked loop block 320 may generate aphase-shifted signal 90 degrees out of phase with frequency referenceoutput signal, may multiply this phase-shifted signal with the measureddisplacement in the first mode, and may process the result with alow-pass filter. The DC component of the product of the measureddisplacement and the phase-shifted sinusoidal signal will be zero if themeasured displacement in the first mode is perfectly in phase with thefrequency reference output signal, and it will be non-zero andproportional to the phase error (for a small phase error) when themeasured displacement in the first mode is not perfectly in phase withthe frequency reference output signal. In other embodiments, therelative phase of the measured displacement in the first mode and thefrequency reference output signal may be measured using other methods,e.g., by fitting each with a linear combination of a sine function and acosine function. A phase error may then be calculated by taking thedifference between (i) the phase difference between the measureddisplacement in the first mode and the frequency reference output signaland (ii) a first phase target (i.e., a target phase difference or “phasesetpoint”). Once a phase error has been calculated, a phase correctionsignal may be generated from the phase error by processing the phaseerror with a PID controller (or with a loop filter and then a PIDcontroller), either in the phase locked loop block 320 or in the firstautomatic gain control block 315.

The automatic gain control block 315 may then generate a digital drivesignal, that tends to reduce the amplitude error and the phase error,from the amplitude correction signal, the phase correction signal, thephase-shifted signal and the frequency reference output signal. Thisdrive signal may have an amplitude proportional to the amplitudecorrection signal (or proportional to the amplitude correction signalplus a constant offset) and a phase set by the phase correction signal.For example, when the phase error is zero, the phase of the drive signalmay be zero (i.e., it may produce a force that leads the displacement by90 degrees), and when the phase error is not zero, the phase of thedrive signal may be proportional to the phase correction signal.Similarly, the amplitude of the drive signal, when the amplitude erroris zero, may be just sufficient to counteract mechanical loss in theresonator, so that the amplitude of the motion in the first mode remainsconstant. When the amplitude correction signal is positive, theamplitude of the drive signal may be greater, and when the amplitudecorrection signal is negative, the amplitude of the drive signal may besmaller. The drive signal may be applied to the first drive electrode110, to produce a corresponding force on the resonator.

The second control loop may similarly include a second transimpedanceamplifier (TIA) 355, a second analog to digital converter 360, a secondautomatic gain control block 365, a second phase locked loop block 370,a second digital to analog converter 375, and a second driver 380. Theamplitude and phase of the displacement in the second mode may becontrolled in an analogous manner to have a particular amplitude, and aparticular phase relative to the output of the frequency reference 210.In one embodiment the second mode is controlled to oscillate with aphase that is 90 degrees different from that of the first mode (i.e.,the oscillation of the second mode is locked to a second phase targetthat differs by 90 degrees from the first phase target), and with anamplitude that is about 10% of that of the first mode. When the DRGrotates, energy couples from the first mode into the second mode with aphase that is 90 degrees out of phase with the nominal oscillation ofthe second mode, resulting in a phase error in the second mode that isthen suppressed by the second control loop. The rate of rotation maythen be inferred from the phase error signal or by the phase correctionsignal in the second loop. In one embodiment the first and second phasetargets, and the first and second amplitude targets can be individuallyset, e.g., they are programmable. In some embodiments, the first andsecond amplitude targets may be changed in real time, i.e., duringoperation, and the gyroscope may be operated in a mode in which they areperiodically interchanged, i.e., during alternating first and secondtime intervals either the second amplitude target is about 10% of thefirst, or the first amplitude target is about 10% of the second, so thateach amplitude target alternates periodically between the first andsecond values.

In another embodiment, shown in FIG. 4, the signal used to drive thefirst mode has a constant phase (e.g., zero degrees) with respect to theoutput of the frequency reference 210, and the amplitude of theoscillations in the first mode is controlled by an automatic gaincontrol circuit (AGC) that detects the amplitude of the signal at asense electrode S1 with an amplitude detector 410 (which may include ademodulator and a low-pass filter), processes the output with a PIDcontroller 415, and drives the drive electrode D1 with the output of amultiplier 420 which generates the product of the PID controller outputtarget amplitude and the AC signal from frequency reference 210, theinput to which is the signal from the output of the frequency reference210. In one embodiment the amplitude detector has a demodulator (fed bythe frequency reference 210, as shown in FIG. 4) followed by a low passloop filter and the PID controller 430. The demodulator may be drivenoff the frequency reference. In other embodiments the amplitude detector410 may not require a frequency reference and the connection (shown inFIG. 4) from the frequency reference 210 may be absent. Phase control inthe embodiment of FIG. 4 is accomplished by tuning the natural frequencyof the first normal mode by applying a slowly varying feedback signal(or “bias voltage”) to the tuning electrode T1. This feedback signal isgenerated by measuring, with a phase detector 425, the phase differencebetween the output of the frequency reference 210 and the signal at thesense electrode S1, and processing the phase error with a PID controller430.

A similar circuit (duplicate of 430, 425, 410, and 415 and not shown inFIG. 4, for clarity) may control the amplitude and phase of the secondnormal mode. In one embodiment the amplitude of the second normal modeis controlled (by suitable selection of the second amplitude target) tobe less than that of the first normal mode (e.g., 1/10^(th) of that ofthe first normal mode), and the phase is controlled (e.g., by phaseshifting the signal from the frequency reference 210) to be 90 degreesout of phase with that of the first normal mode.

FIG. 5A shows an example of the natural frequencies of the first andsecond normal modes in embodiments in which these natural frequenciesare not controlled. In the embodiment of FIG. 4, using an externalfrequency to tune the natural frequencies of the first and second normalmodes by phase locking as described above, results in both naturalfrequencies being controlled (by the application of respective tuningvoltages) to be the same as the frequency at the output of the frequencyreference 210, as illustrated in FIG. 5B, and to be correspondinglystable. This may result in stable bias, i.e., in low bias drift.

Referring to FIG. 6, in one embodiment an improvement in stability maybe characterized by a lower Allan deviation as a function of integrationtime, compared to related art embodiments not using a stable frequencyreference. A family of first curves 610 corresponds to performance,measured in each case as an Allan deviation, that may be expected fromrelated art systems operating without a stable frequency reference. Twosecond curves 620 define an envelope of improved performance curves thatmay be expected for a gyroscope employing embodiments of the presentinvention, for various grades of high stability frequency references.

In some embodiments, two pairs of nominally degenerate normal modes,e.g., a first pair each having a mode number of n=2, and a second paireach having a mode number of n=3, may be operated (i.e., driven andsensed) simultaneously or concurrently to provide an improvement indynamic range. FIG. 7 shows an undeformed resonator 710, along with theshape 720 that it may take when deformed in the shape of an n=2 mode andthe shape 730 that it may take when deformed in the shape of an n=3mode.

Referring to FIG. 8, in one embodiment a Coriolis vibratory gyroscope(CVG) includes a sensor head 810, a coarse readout circuit 815, a finereadout circuit 820 and a summing circuit 825, generating a high dynamicrange signal at an output 830. For example, the first pair of normalmodes (the n=2 modes) may be sensed by a coarse readout circuit 815having a scale factor selected to allow the sensing circuitry to operateat rotation rates (for the DRG) of up to ±900 degrees per second. Here,the “scale factor” refers to the ratio of the rate-indicating output ofthe gyroscope (which may be an analog voltage or a digital number) tothe rotation rate (e.g., in degrees per second). The selection of ascale factor suitable for operation at high angular rates (e.g., 900degrees per second) may have the effect that the resolution of thegyroscope may be less fine than it would be if the scale factor wereselected to accommodate only a smaller angular rate.

The rate-indicating output from the coarse readout circuit 815 may befed, as an offset or bias, into the fine readout circuit 820 (which maydrive and sense the second pair of normal modes, e.g., the n=3 modes),so that the output of the fine readout circuit 820 ranges only over asignificantly smaller range of angular rates. For example, the systemmay include two copies of the readout circuit of FIG. 3, one operatingas a coarse readout circuit and the other operating as the fine readoutcircuit. The rate-indicating output of the coarse readout circuit maythen be (or be proportional to), for example, the phase error signal orthe phase correction signal in the coarse readout circuit. In oneembodiment, the scale factor for the second pair of modes is larger thanthat for the first pair of modes by a factor of approximately (about)2¹⁹, i.e., a factor of approximately (about) 524,288, so that the secondpair of modes is configured to sense angular rates with a magnitude ofless than 0.002 degrees per second. Each readout circuit may include arespective frequency divider 340, with the factors by which thefrequency is divided being selected so that the respective outputfrequencies of the two frequency dividers 340 correspond to therespective natural frequencies of the two pairs of normal modes.

Several methods may be employed to introduce an offset or bias into thefine readout circuit 820. In one embodiment, the output of the coarsereadout circuit 815 is modulated, by a suitable analog or digitalmodulation circuit, to generate the signal expected at a point in thesecond control loop of the fine readout circuit 820, and the output ofthe modulation circuit is added to the signal from this point in theloop to generate a signal containing only a residual signal,corresponding to the difference between the angular rate and the coarsemeasurement of the angular rate generated by the coarse readout circuit815. This signal may be suitable for being measured or calculated withsubstantially finer resolution than the output of the coarse readoutcircuit 815.

In another embodiment the output of the coarse readout circuit 815 maybe used to adjust the respective drive frequencies of the modes of thefine readout circuit 820 (e.g., the n=3 modes), to introduce a bias thatcancels a substantial portion of the signal, again leaving only a smallresidual signal suitable for being measured with substantially finerresolution than the output of the coarse readout circuit 815.

The techniques of embodiments of the present invention may be applied toother sensors such as accelerometers and magnetometers, e.g., using anexternal frequency reference to stabilize the control loops used toperform a readout operation of the desired quantity to be sensed by aMEMS resonator in a manner analogous to the readout of rotation rate ina MEMS CVG resonator. In these embodiments, there may be fewer or moretotal control loops employing the frequency stabilization concept. Forexample, an accelerometer or magnetometer may include a resonator havinga natural frequency that is adjustable using a natural frequency controlsignal, e.g., by the application of a bias voltage to a tuningelectrode. A stable frequency reference may be used to drive theresonator, and a phase difference between the drive signal and themotion of the resonator may be measured. A feedback signal derived fromthe difference between (i) the phase difference and (ii) a programmablephase target may be connected as a natural frequency control signal,tending to make the phase difference equal to the programmable phasetarget.

The techniques of embodiments of the present invention may be applied toa cluster of multiple sensors sharing a common frequency reference usedfor stabilizing the output signal. The cluster of sensors may becomposed of sensors of varying types. For example, a stabilized 3 axisgyroscope cluster may be formed by 3 (or more) single axis gyroscopesarranged sharing a single stable frequency reference. An inertialmeasurement unit (IMU) may be formed by arranging 3 (or more) stabilizedgyroscopes and 3 (or more) stabilized accelerometers sharing a singlestable frequency reference. Finally, a complete IMU plus magneticcompass navigation sensor unit may be formed by arranging 3 (or more)stabilized gyroscopes, 3 (or more) stabilized accelerometers, and 3 (ormore) stabilized magnetometers sharing a single stable frequencyreference.

It will be understood that, although the terms “first”, “second”,“third”, etc., may be used herein to describe various elements,components, regions, layers and/or sections, these elements, components,regions, layers and/or sections should not be limited by these terms.These terms are only used to distinguish one element, component, region,layer or section from another element, component, region, layer orsection. Thus, a first element, component, region, layer or sectiondiscussed below could be termed a second element, component, region,layer or section, without departing from the spirit and scope of theinventive concept.

Spatially relative terms, such as “beneath”, “below”, “lower”, “under”,“above”, “upper” and the like, may be used herein for ease ofdescription to describe one element or feature's relationship to anotherelement(s) or feature(s) as illustrated in the figures. It will beunderstood that such spatially relative terms are intended to encompassdifferent orientations of the device in use or in operation, in additionto the orientation depicted in the figures. For example, if the devicein the figures is turned over, elements described as “below” or“beneath” or “under” other elements or features would then be oriented“above” the other elements or features. Thus, the example terms “below”and “under” can encompass both an orientation of above and below. Thedevice may be otherwise oriented (e.g., rotated 90 degrees or at otherorientations) and the spatially relative descriptors used herein shouldbe interpreted accordingly. In addition, it will also be understood thatwhen a layer is referred to as being “between” two layers, it can be theonly layer between the two layers, or one or more intervening layers mayalso be present.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the inventiveconcept. As used herein, the terms “substantially,” “about,” and similarterms are used as terms of approximation and not as terms of degree, andare intended to account for the inherent deviations in measured orcalculated values that would be recognized by those of ordinary skill inthe art. As used herein, the term “major component” means a componentconstituting at least half, by weight, of a composition, and the term“major portion”, when applied to a plurality of items, means at leasthalf of the items.

As used herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising”, when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof. As used herein, the term “and/or”includes any and all combinations of one or more of the associatedlisted items. Expressions such as “at least one of,” when preceding alist of elements, modify the entire list of elements and do not modifythe individual elements of the list. Further, the use of “may” whendescribing embodiments of the inventive concept refers to “one or moreembodiments of the present invention”. Also, the term “exemplary” isintended to refer to an example or illustration. As used herein, theterms “use,” “using,” and “used” may be considered synonymous with theterms “utilize,” “utilizing,” and “utilized,” respectively.

It will be understood that when an element or layer is referred to asbeing “on”, “connected to”, “coupled to”, or “adjacent to” anotherelement or layer, it may be directly on, connected to, coupled to, oradjacent to the other element or layer, or one or more interveningelements or layers may be present. In contrast, when an element or layeris referred to as being “directly on”, “directly connected to”,“directly coupled to”, or “immediately adjacent to” another element orlayer, there are no intervening elements or layers present.

Any numerical range recited herein is intended to include all sub-rangesof the same numerical precision subsumed within the recited range. Forexample, a range of “1.0 to 10.0” is intended to include all subrangesbetween (and including) the recited minimum value of 1.0 and the recitedmaximum value of 10.0, that is, having a minimum value equal to orgreater than 1.0 and a maximum value equal to or less than 10.0, suchas, for example, 2.4 to 7.6. Any maximum numerical limitation recitedherein is intended to include all lower numerical limitations subsumedtherein and any minimum numerical limitation recited in thisspecification is intended to include all higher numerical limitationssubsumed therein.

Any digital circuit employed in embodiments of the present invention,such as the digital control and synthesis circuit 352, may beimplemented with a processor. The term “processor” is used herein toinclude any combination of hardware, firmware, and software, employed toprocess data or digital signals. Processing unit hardware may include,for example, application specific integrated circuits (ASICs), generalpurpose or special purpose central processing units (CPUs), digitalsignal processors (DSPs), graphics processing units (GPUs), andprogrammable logic devices such as field programmable gate arrays(FPGAs).

Although exemplary embodiments of a high stability angular sensor havebeen specifically described and illustrated herein, many modificationsand variations will be apparent to those skilled in the art.Accordingly, it is to be understood that a high stability angular sensorconstructed according to principles of this invention may be embodiedother than as specifically described herein. The invention is alsodefined in the following claims, and equivalents thereof.

What is claimed is:
 1. An angular sensor, comprising: a Coriolisvibratory gyroscope (CVG) resonator, configured to oscillate in a firstnormal mode and in a second normal mode, the first normal mode and thesecond normal mode having the same mode number; a frequency referenceconfigured to generate a reference signal; and a first phase controlcircuit configured to: measure a first phase difference between: a firstphase target, and the difference between: a phase of a mechanicaloscillation of the first normal mode and a phase of the referencesignal; apply a first phase correction signal to the CVG resonator, toreduce the first phase difference; and a second phase control circuitconfigured to: measure a second phase difference between: a second phasetarget, and the difference between: a phase of a mechanical oscillationof the second normal mode and the phase of the reference signal; andapply a second phase correction signal to the CVG resonator, to reducethe second phase difference.
 2. The angular sensor of claim 1, whereinthe first phase target and the second phase target are programmable. 3.The angular sensor of claim 1, further comprising a first amplitudecontrol circuit configured to: measure a first amplitude differencebetween: a first amplitude target, and the amplitude of the mechanicaloscillation of the first normal mode, and apply a first amplitudecorrection signal to the CVG resonator, to reduce the first amplitudedifference.
 4. The angular sensor of claim 3, further comprising asecond amplitude control circuit configured to: measure a secondamplitude difference between: a second amplitude target, and theamplitude of the mechanical oscillation of the second normal mode, andapply a second amplitude correction signal to the CVG resonator, toreduce the second amplitude difference.
 5. The angular sensor of claim4, wherein the first amplitude target and the second amplitude targetare programmable.
 6. The angular sensor of claim 4, wherein the firstamplitude target is about 1/10^(th) of the second amplitude target. 7.The angular sensor of claim 1, wherein the frequency reference comprisesan atomic frequency reference.
 8. The angular sensor of claim 7, whereinthe atomic frequency reference is a rubidium clock.
 9. The angularsensor of claim 7, wherein the atomic frequency reference is achip-scale atomic clock (CSAC).
 10. The angular sensor of claim 1,wherein the first phase control circuit is configured to apply a firstphase correction signal to the CVG resonator by adjusting a naturalfrequency of the first normal mode.
 11. The angular sensor of claim 1,wherein the first phase control circuit is configured to adjust anatural frequency of the first normal mode by applying a bias voltage toa first tuning electrode of the CVG resonator.
 12. The angular sensor ofclaim 1, wherein the second phase control circuit is configured toadjust a natural frequency of the second normal mode by applying a biasvoltage to a second tuning electrode of the CVG resonator.
 13. Theangular sensor of claim 12, further comprising a first amplitude controlcircuit configured to: measure a first amplitude difference between: afirst amplitude target, and the amplitude of the mechanical oscillationof the first normal mode, and apply a first amplitude correction signalto the CVG resonator, to reduce the first amplitude difference.
 14. Theangular sensor of claim 13, further comprising a second amplitudecontrol circuit configured to: measure a second amplitude differencebetween: a second amplitude target, and the amplitude of the mechanicaloscillation of the second normal mode, and apply a second amplitudecorrection signal to the CVG resonator, to reduce the second amplitudedifference.
 15. The angular sensor of claim 14, wherein the firstamplitude target and the second amplitude target are programmable. 16.The angular sensor of claim 14, wherein the first amplitude target isabout 1/10^(th) of the second amplitude target.
 17. The angular sensorof claim 14, wherein the first amplitude control circuit, and the secondamplitude control circuit are configured to interchange the values ofthe first amplitude target and the second amplitude target duringoperation.
 18. A sensor cluster comprising: a plurality of the angularsensors of claim 1, configured to share a common frequency reference.